A. Rozkosz

activity

20102026

most citedDirichlet forms and semilinear elliptic equations with measure data

53 citations · 157 across the 23 of their papers we have counts for

collaborators

26 papers

math.AP2026

Stability of Solutions to Semilinear Exterior Dirichlet Problems under Convergence of Lévy Symbols

Tomasz Klimsiak, Andrzej Rozkosz, Leszek Słomiński

We study stability of semilinear exterior Dirichlet problems driven by possibly nonsymmetric Levy operators. Let $L^{n}$ and $L$ have Lévy-Khintchine symbols $ψ_{n}$ and $ψ$ , respectiv…

math.AP2025

Nonlinear Hardy-Stein type identities for harmonic functions relative to symmetric integro-differential operators

Tomasz Klimsiak, Andrzej Rozkosz

We show identities of Hardy-Stein type for harmonic functions relative to integro-differential operators corresponding to general symmetric regular Dirichlet forms satisfying the a…

math.AP2025

Robin problem with measure data and singular nonlinearities on the boundary

Andrzej Rozkosz

We consider the Robin problem for a uniformly elliptic divergence operator with measure data on the right-hand side of the equation and an absorption term on the boundary involving…

math.AP2024

Stability of solutions of semilinear evolution equations with integro-differential operators

Andrzej Rozkosz, Leszek Słomiński

We consider solutions of the Cauchy problem for semilinear equations with (possibly) different Lévy operators. We provide various results on their convergence under the assumption…

math.AP2024

Poisson equation with measure data, reconstruction formula and Doob classes of processes

Andrzej Rozkosz, Tomasz Klimsiak

We consider the Dirichlet problem for equation involving a general operator associated with a symmetric transient regular Dirichlet form and bounded Borel measure on the right-hand…

math.AP2023★ 6 cited

Dirichlet problem for semilinear partial integro-differential equations: the method of orthogonal projection

Tomasz Klimsiak, Andrzej Rozkosz

We study the Dirichlet problem for semilinear equations on general open sets with measure data on the right-hand side and irregular boundary data. For this purpose we develop the c…

math.AP2023

Reflected Skorokhod equations and the Neumann boundary value problem for elliptic equations with Levy-type operators

Andrzej Rozkosz, Leszek Slominski

We consider Neumann problem for linear elliptic equations involving integro-differential operators of Levy-type. We show that suitably defined viscosity solutions have probabilisti…

math.AP2022★ 1 cited

On approximation of the Dirichlet problem for divergence form operator by Robin problems

Andrzej Rozkosz, Leszek Slominski

We show, that under natural assumptions, solutions of Dirichlet problems for uniformly elliptic divergence form operator can be approximated pointwise by solutions of some versions…

math.PR2020

Long-time asymptotic behaviour of the value function in nonlinear stopping problems

Tomasz Klimsiak, Andrzej Rozkosz

We provide general conditions ensuring that the value functions of some nonlinear stopping problems with finite horizon converge to the value functions of the corresponding problem…

math.PR2019★ 1 cited

On perpetual American options in a multidimensional Black-Scholes model

Andrzej Rozkosz

We consider the problem of pricing perpetual American options written on dividend-paying assets whose price dynamics follow a multidimensional Black and Scholes model. For convex L…

math.AP2018★ 2 cited

Smooth measures and capacities associated with nonlocal parabolic operators

Tomasz Klimsiak, Andrzej Rozkosz

We consider a family ${L_{t}, t \in [0, T]}$ of closed operators generated by a family of regular (non-symmetric) Dirichlet forms ${(B^{(t)}, V), t \in [0, T]}$ on $L^{2} (E; m)$ . We show…

math.AP2018

On the structure of diffuse measures for parabolic capacities

Tomasz Klimsiak, Andrzej Rozkosz

Let $Q = (0, T) \times Ω$ , where $Ω$ is a bounded open subset of $R^{d}$ . We consider the parabolic $p$ -capacity on $Q$ naturally associated with the usual $p$ -Laplacian. Droniou…

math.AP2018★ 3 cited

On semilinear elliptic equations with diffuse measures

Tomasz Klimsiak, Andrzej Rozkosz

We consider semilinear equation of the form $- Lu = f (x, u) + μ$ , where $L$ is the operator corresponding to a transient symmetric regular Dirichlet form $E$ , $μ$ is a diffuse…

math.AP2016★ 4 cited

Renormalized solutions of semilinear elliptic equations with general measure data

Tomasz Klimsiak, Andrzej Rozkosz

In the paper, we first propose a definition of renormalized solution of semilinear elliptic equation involving operator corresponding to a general (possibly nonlocal) symmetric reg…

math.AP2016★ 1 cited

Systems of semilinear parabolic variational inequalities with time-dependent convex obstacles

Tomasz Klimsiak, Andrzej Rozkosz, Leszek Slominski

We consider a system of seminlinear parabolic variational inequalities with time-dependent convex obstacles. We prove the existence and uniqueness of its solution. We also provide…

math.PR2016

Nonlinear parabolic SPDEs involving Dirichlet operators

Tomasz Klimsiak, Andrzej Rozkosz

We study the problem of existence, uniqueness and regularity of probabilistic solutions of the Cauchy problem for nonlinear stochastic partial differential equations involving oper…

math.AP2016★ 1 cited

Large time behaviour of solutions to parabolic equations with Dirichlet operators and nonlinear dependence on measure data

Tomasz Klimsiak, Andrzej Rozkosz

We study large time behaviour of solutions of the Cauchy problem for equations of the form $\partial_{t} u - Lu + λ u = f (x, u) + g (x, u) \cdot μ$ , where $L$ is the operator associated with a reg…

math.PR2016★ 5 cited

The valuation of American options in a multidimensional exponential Levy model

Tomasz Klimsiak, Andrzej Rozkosz

We consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follows a multidimensional exponential Levy model. We carefully exam…

math.AP2015★ 18 cited

Renormalized solutions of semilinear equations involving measure data and operator corresponding to Dirichlet form

Tomasz Klimsiak, Andrzej Rozkosz

We generalize the notion of renormalized solution to semilinear elliptic and parabolic equations involving operator associated with general (possibly nonlocal) regular Dirichlet fo…

math.FA2014★ 9 cited

On the structure of bounded smooth measures associated with a quasi-regular Dirichlet form

Tomasz Klimsiak, Andrzej Rozkosz

We consider a quasi-regular Dirichlet form. We show that a bounded signed measure charges no set of zero capacity associated with the form if and only if the measure can be decompo…

math.PR2013★ 19 cited

Reflected BSDEs in time-dependent convex regions

Tomasz Klimsiak, Andrzej Rozkosz, Leszek Slominski

We prove existence and uniqueness of solutions of reflected backward stochastic differential equations in time-dependent adapted and càdlàg convex regions $\mathcal{D}=\{D_t;t\in[0…

math.AP2013★ 15 cited

Semilinear elliptic equations with measure data and quasi-regular Dirichlet forms

Tomasz Klimsiak, Andrzej Rozkosz

We are mainly concerned with equations of the form $- Lu = f (x, u) + μ$ , where $L$ is an operator associated with a quasi-regular possibly nonsymmetric Dirichlet form, $f$ satisfies the…

math.PR2013★ 6 cited

The early exercise premium representation for American options on multiply assets

Tomasz Klimsiak, Andrzej Rozkosz

In the paper we consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follow the classical multidimensional Black and Scholes…

math.AP2013★ 13 cited

Obstacle problem for semilinear parabolic equations with measure data

Tomasz Klimsiak, Andrzej Rozkosz

We consider the obstacle problem with two irregular reflecting barriers for the Cauchy-Dirichlet problem for semilinear parabolic equations with measure data. We prove the existenc…