Tomasz Klimsiak

activity

20092026

most citedDirichlet forms and semilinear elliptic equations with measure data

53 citations · 217 across the 49 of their papers we have counts for

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25 papers · 1 filter

math.PR2026

A Quantitative Characterization of the Mokobodzki Condition

Tomasz Klimsiak, Maurycy Rzymowski

We establish a quantitative characterization of the Mokobodzki condition for two adapted càdlàg barriers on an arbitrary filtered probability space. For every $p \geq 1$ , we introduc…

math.PR2024

Mokobodzki's intervals: an approach to Dynkin games when value process is not a semimartingale

Tomasz Klimsiak, Maurycy Rzymowski

We study Dynkin games governed by a nonlinear $E^{f}$ -expectation on a finite interval $[0, T]$ , with payoff càdlàg processes $L, U$ of class (D) which are not imposed to satis…

math.PR2024

Homogenization of stable-like operators with random, ergodic coefficients

Tomasz Klimsiak, Tomasz Komorowski, Lorenzo Marino

We show homogenization for a family of $R^{d}$ -valued stable-like processes $(X_{t}^{ε; θ})_{t \geq 0}$ , $ε \in (0, 1]$ , whose (random) Fourier symbols equal $q_ε(x,ξ;θ)=\frac{1}{ε^…

math.PR2022

A priori estimates for multidimensional BSDEs with integrable data

Tomasz Klimsiak, Maurycy Rzymowski

We study Backward Stochastic Differential Equations on a probability space equipped with a Brownian filtration. We assume that the terminal value and the generator at zero are mere…

math.PR2022

Nonlinear BSDEs with two optional Doob's class barriers satisfying weak Mokobodzki's condition and extended Dynkin games

Tomasz Klimsiak, Maurycy Rzymowski

We study reflected backward stochastic differential equation (RBSDEs) on the probability space equipped with a Brownian motion. The main novelty of the paper lies in fact that we c…

math.PR2021

Nonlinear BSDEs in general filtration with drivers depending on the martingale part of a solution

Tomasz Klimsiak, Maurycy Rzymowski

In the present paper, we consider multidimensional nonlinear backward stochastic differential equations (BSDEs) with a driver depending on the martingale part $M$ of a solution. We…

math.PR2021

Hopf type lemmas for subsolutions of integro-differential equations

Tomasz Klimsiak, Tomasz Komorowski

In the paper we prove a generalization of the Hopf lemma for weak subsolutions of the equation: $- A u + c u = 0$ in $D$ , for a wide class of Lévy type integro-differential operators $A$ ,…

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.PR2020

Reflected BSDEs with two optional barriers and monotone coefficient on general filtered space

Tomasz Klimsiak, Maurycy Rzymowski

We consider reflected backward stochastic differential equations with two optional barriers of class (D) satisfying Mokobodzki's separation condition and coefficient which is only…

math.PR2018

Reflected backward stochastic differential equations with two optional barriers

Tomasz Klimsiak, Maurycy Rzymowski, Leszek Słomiński

We consider reflected backward stochastic differential equations with two general optional barriers. The solutions to these equations have the so-called regulated trajectories, i.e…

math.PR2018

Reflected BSDEs with monotone generator

Tomasz Klimsiak

We give necessary and sufficient condition for existence and uniqueness of $L^{p}$ -solutions of reflected BSDEs with continuous barrier, generator monotone with respect to…

math.PR2018

BSDEs with monotone generator and two irregular reflecting barriers

Tomasz Klimsiak

We consider BSDEs with two reflecting irregular barriers. We give necessary and sufficient conditions for existence and uniqueness of $L^{p}$ solutions for equations with…

math.PR2018★ 1 cited

Non-semimartingale solutions of reflected BSDEs and applications to Dynkin games

Tomasz Klimsiak

We introduce a new class of reflected backward stochastic differential equations with two càdlàg barriers, which need not satisfy any separation conditions. For that reason, in gen…

math.PR2016

Systems of quasi-variational inequalities related to the switching problem

Tomasz Klimsiak

We prove the existence of weak solution for a system of quasi-variational inequalities related to a switching problem with dynamic driven by operator associated with a semi-Dirichl…

math.PR2016

Reflected BSDEs with regulated trajectories

Tomasz Klimsiak, Maurycy Rzymowski, Leszek Słomiński

We consider reflected backward stochastic different equations with optional barrier and so-called regulated trajectories, i.e trajectories with left and right finite limits. We pro…

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.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.PR2015

Quasi-regular Dirichlet forms and the obstacle problem for elliptic equations with measure data

Tomasz Klimsiak

We consider the obstacle problem with irregular barriers for semilinear elliptic equation involving measure data and operator corresponding to a general quasi-regular Dirichlet for…

math.PR2014★ 38 cited

Reflected BSDEs on Filtered Probability Spaces

Tomasz Klimsiak

We study the problem of existence and uniqueness of solutions of backward stochastic differential equations with two reflecting irregular barriers, $L^{p}$ data and generators satisf…

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.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.PR2010

On backward stochastic differential equations approach to valuation of American options

Tomasz Klimsiak, Andrzej Rozkosz

We consider the problem of valuation of American (call and put) options written on a dividend paying stock governed by the geometric Brownian motion. We show that the value functio…

math.PR2010

Strong solutions of semilinear parabolic equations with measure data and generalized backward stochastic differential equations

Tomasz Klimsiak

We prove that under natural assumptions on the data strong solutions in Sobolev spaces of semilinear parabolic equations in divergence form involving measure on the right-hand side…

math.PR2010★ 2 cited

On time-dependent functionals of diffusions corresponding to divergence form operators

Tomasz Klimsiak

We consider additive functionals as a time and space-dependent function of a diffusion corresponding to nonhomogeneous uniformly elliptic divergence form operator. We show that if…