51 citations · 143 across the 18 of their papers we have counts for
19 papers
Intrusive and Non-Intrusive Polynomial Chaos Approximations for a Two-Dimensional Steady State Navier-Stokes System with Random Forcing
S. V. Lototsky, R. Mikulevicius, B. L. Rozovsky
While convergence of polynomial chaos approximation for linear equations is relatively well understood, a lot less is known for non-linear equations. The paper investigates this co…
On the Cauchy problem for stochastic integro-differential equations with radially O-regularly varying Levy measure
R. Mikulevicius, C. Phonsom
Parabolic integro-differential nondegenerate Cauchy problem is considered in the scale of L_{p} spaces of functions whose regularity is defined by a Levy measure with O-regulary va…
On some cadlaguity moment estimates of stochastic jump processes
R. Mikulevicius, Fanhui Xu
Using the results of X. Fernique on the compactness of distributions of cadlag random functions, we derive some cadlaguity moment estimates for stochastic processes with jumps.
On the Cauchy problem for nondegenerate parabolic integro-differential equations in the scale of generalized Hölder spaces
R. Mikulevicius, Fanhui Xu
Parabolic integro-differential non degenerate Cauchy problem is considered in the scale of Hölder spaces of functions whose regularity is defined by a radially O-regularly varying…
On the Cauchy problem for stochastic integrodifferential parabolic equations in the scale of Lp-spaces of generalized smoothness
R. Mikulevicius, C. Phonsom
Stochastic parabolic integro-differential problem is considered in the whole space. By verifying Hörmander condition, the existence and uniqueness is proved in Lp-spaces of functio…
On the Cauchy problem for integro-differential equations in the scale of spaces of generalized smoothness
R. Mikulevicius, C. Phonsom
Parabolic integro-differential model Cauchy problem is considered in the scale of Lp -spaces of functions whose regularity is defined by a scalable Levy measure. Existence and uniq…
On the rate of convergence of strong Euler approximation for SDEs driven by Levy processes
R. Mikulevicius, Fanhui Xu
SDE driven by an -stable process, with Lipshitz continuous coefficient and -Hölder drift is considered. The existence and uniqueness of a strong solution…
On Lp -theory for parabolic and elliptic integro-differential equations with scalable operators in the whole space
R. Mikulevicius, C. Phonsom
Elliptic and parabolic integro-differential model problems are considered in the whole space. By verifying Hörmander condition, the existence and uniqueness is proved in L_{p}-spac…
On Some Properties of Space Inverses of Stochastic Flows
James-Michael Leahy, Remigijus Mikulevicius
We derive moment estimates and a strong limit theorem for space inverses of stochastic flows generated by jump SDEs with adapted coefficients in weighted Hölder norms using the Sob…
On Degenerate Linear Stochastic Evolution Equations Driven by Jump Processes
James-Michael Leahy, Remigijus Mikulevicius
We prove the existence and uniqueness of solutions of degenerate linear stochastic evolution equations driven by jump processes in a Hilbert scale using the variational framework o…
On Classical Solutions of Linear Stochastic Integro-Differential Equations
James-Michael Leahy, Remigijus Mikulevicius
We prove the existence of classical solutions to parabolic linear stochastic integro-differential equations with adapted coefficients using Feynman-Kac transformations, conditionin…
On the Cauchy problem for integro-differential operators in Sobolev classes and the martingale problem
R. Mikulevicius, H. Pragarauskas
The existence and uniqueness in Sobolev spaces of solutions of the Cauchy problem to parabolic integro-differential equation of the order α\in(0,2) is investigated. The principal p…
On the rate of convergence of simple and jump-adapted weak Euler schemes for Levy driven SDEs
R. Mikulevicius
The paper studies the rate of convergence of the weak Euler approximation for solutions to possibly completely degenerate SDEs driven by Levy processes, with Hoelder-continuous coe…
On the Cauchy problem for integro-differential operators in Hölder classes and the uniqueness of the martingale problem
R. Mikulevicius, H. Pragarauskas
The existence and uniqueness in Hölder spaces of solutions of the Cauchy problem to parabolic integro-differential equation of the order α\in(0,2) is investigated. The principal pa…
On the Rate of Convergence of Weak Euler Approximation for Nondegenerate SDEs Driven by Levy Processes
R. Mikulevicius, C. Zhang
The paper studies the rate of convergence of the weak Euler approximation for solutions to SDEs driven by Levy processes, with Hoelder-continuous coefficients. It investigates the…
On L_p- theory for stochastic parabolic integro-differential equations
R. Mikulevicius, H. Pragarauskas
The existence and uniqueness in fractional Sobolev spaces of the Cauchy problem to a stochastic parabolic integro-differential equation is investigated. A model problem with coeffi…
On the rate of convergence of weak Euler approximation for non-degenerate SDEs
R. Mikulevicius, C. Zhang
The paper estimates the rate of convergence of the weak Euler approximation for the solutions of SDEs with Hoelder continuous coefficients driven by point and martingale measures.…
Model problem for integro-differential Zakai equation with discontinuous observation processes in Hölder spaces
R. Mikulevicius, H. Pragarauskas
The existence and uniqueness of solutions of the Cauchy problem to a a stochastic parabolic integro-differential equation is investigated. The equattion considered arises in nonlin…
On L_{p}-estimates of some singular integrals related to jump processes
R. Mikulevicius, H. Pragarauskas
We estimate fractional Sobolev and Besov norms of some singular integrals arising in the model problem for the Zakai equation with discontinuous signal and observation.