Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 3

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: jump processes

Sortuj według:

Ogranicz wyniki do:

A Note on Existence of Global Solutions and Invariant Measures for Jump Sdes with Locally One-Sided Lipschitz Drift

Majka Mateusz B.

Probability and Mathematical Statistics

2020

Vol. 40, Fasc. 1

37--55

We extend some methods developed by Albeverio, Brzeźniak and Wu and we show how to apply them in order to prove existence of global strong solutions of stochastic differential equations with jumps, under a local one-sided Lipschitz condition on the drift (also known as a monotonicity condition) and a local Lipschitz condition on the diffusion and jump coefficients, while an additional global one-sided linear growth assumption is satisfied. Then we use these methods to prove existence of invariant measures for a broad class of such equations.

Embedded Markov Chain Approximations in Skorokhod Topologies

Böttcher Björn

Probability and Mathematical Statistics

2019

Vol. 39, Fasc. 2

259--277

We prove a J1-tightness condition for embedded Markov chains and discuss four Skorokhod topologies in a unified manner. To approximate a continuous time stochastic process by discrete time Markov chains, one has several options to embed the Markov chains into continuous time processes. On the one hand, there is a Markov embedding which uses exponential waiting times. On the other hand, each Skorokhod topology naturally suggests a certain embedding. These are the step function embedding for J1, the linear interpolation embedding for M1, the multistep embedding for J2 and a more general embedding for M2. We show that the convergence of the step function embedding in J1 implies the convergence of the other embeddings in the corresponding topologies. For the converse statement, a J1-tightness condition for embedded time-homogeneous Markov chains is given. Additionally, it is shown that J1 convergence is equivalent to the joint convergence in M1 and J2.

Nonlinear filtering for Markov systems with delayed observations

Calzolari A., Florchinger P., Nappo G.

International Journal of Applied Mathematics and Computer Science

2009

Vol. 19, no 1

49-57

This paper deals with nonlinear filtering problems with delays, i.e., we consider a system (X,Y ), which can be represented by means of a system [...], in the sense that [...], where a(t) is a delayed time transformation. We start with X being a Markov process, and then study Markovian systems, not necessarily diffusive, with correlated noises. The interest is focused on the existence of explicit representations of the corresponding filters as functionals depending on the observed trajectory. Various assumptions on the function a(t) are considered.