On one estimation problem.
On one-dimensional diffusion processes living in a bounded space interval
We prove that under some assumptions a one-dimensional Itô equation has a strong solution concentrated on a finite spatial interval, and the pathwise uniqueness holds.
On pathwise uniqueness and expansion of filtrations
On pathwise uniqueness for stochastic differential equations driven by stable Lévy processes
We study a one-dimensional stochastic differential equation driven by a stable Lévy process of order with drift and diffusion coefficients , . When , we investigate pathwise uniqueness for this equation. When , we study another stochastic differential equation, which is equivalent in law, but for which pathwise uniqueness holds under much weaker conditions. We obtain various results, depending on whether or and on whether the driving stable process is symmetric or not. Our assumptions...
On Poisson-Dirichlet problems with polynomial data
In this note we provide a probabilistic proof that Poisson and/or Dirichlet problems in an ellipsoid in Rd, that have polynomial data, also have polynomial solutions. Our proofs use basic stochastic calculus. The existing proofs are based on famous lemma by E. Fisher which we do not use, and present a simple martingale proof of it as well.
On processes with conditional independent increments and stable convergence in law
On random boundary value problems for ordinary differential equations
On random evolutions induced by countable state space Markov chains
On random orthogonal polynomials.
On regular points in Burgers turbulence with stable noise initial data
On risk reserve under distribution constraints
The purpose of this work is a study of the following insurance reserve model: , t ∈ [0,T], P(η ≥ c) ≥ 1-ϵ, ϵ ≥ 0. Under viability-type assumptions on a pair (p,σ) the estimation γ with the property: is considered.
On rough differential equations.
On sequentially weakly Feller solutions to SPDE’s
A rather general class of stochastic evolution equations in Hilbert spaces whose transition semigroups are Feller with respect to the weak topology is found, and consequences for existence of invariant measures are discussed.
On singular integrals with respect to the gaussian measure
On smoothing properties of transition semigroups associated to a class of SDEs with jumps
We prove smoothing properties of nonlocal transition semigroups associated to a class of stochastic differential equations (SDE) in driven by additive pure-jump Lévy noise. In particular, we assume that the Lévy process driving the SDE is the sum of a subordinated Wiener process (i.e. , where is an increasing pure-jump Lévy process starting at zero and independent of the Wiener process ) and of an arbitrary Lévy process independent of , that the drift coefficient is continuous (but not...
On solutions of general nonlinear stochastic integral equations.
On solutions set of a multivalued stochastic differential equation
We analyse multivalued stochastic differential equations driven by semimartingales. Such equations are understood as the corresponding multivalued stochastic integral equations. Under suitable conditions, it is shown that the considered multivalued stochastic differential equation admits at least one solution. Then we prove that the set of all solutions is closed and bounded.
On Solutions to Stochastic Differential Equations with Discontinuous Drift in Hilbert Space.
On some fractional stochastic integrodifferential equations in Hilbert space.
On some inequalities of local times of iterated stochastic integrals.