List of journals
Browse subjects
About Publisher
Help
Sitemap

Home
Search

VTeX: Solutions for Science Publishing

Classifications: MSC2010-60H10

Detailed search

Journals

Title

Author

Types

Abstract

Keywords

Published

Pages

Volumes

Issues

DOI

Affiliation

Classifications

Search results 38

Order by:

Select: All None Download:

Drift parameter estimation in stochastic differential equation with multiplicative stochastic volatility

Meriem Bel Hadj Khlifa Yuliya Mishura Kostiantyn Ralchenko Mounir Zili

https://doi.org/10.15559/16-VMSTA66

Pub. online: 13 Dec 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 4 (2016), pp. 269–285

Abstract

We consider a stochastic differential equation of the form

\[ dX_{t}=\theta a(t,X_{t})\hspace{0.1667em}dt+\sigma _{1}(t,X_{t})\sigma _{2}(t,Y_{t})\hspace{0.1667em}dW_{t}\]

with multiplicative stochastic volatility, where Y is some adapted stochastic process. We prove existence–uniqueness results for weak and strong solutions of this equation under various conditions on the process Y and the coefficients a, $\sigma _{1}$, and $\sigma _{2}$. Also, we study the strong consistency of the maximum likelihood estimator for the unknown parameter θ. We suppose that Y is in turn a solution of some diffusion SDE. Several examples of the main equation and of the process Y are provided supplying the strong consistency.

Drift parameter estimation in stochastic differential equation with multiplicative stochastic volatility

Meriem Bel Hadj Khlifa Yuliya Mishura Kostiantyn Ralchenko Mounir Zili

https://doi.org/10.15559/16-MSTA66

Pub. online: 13 Dec 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 4 (2016), pp. 269–285

Abstract

We consider a stochastic differential equation of the form

\[ dX_{t}=\theta a(t,X_{t})\hspace{0.1667em}dt+\sigma _{1}(t,X_{t})\sigma _{2}(t,Y_{t})\hspace{0.1667em}dW_{t}\]

Asymptotic behavior of homogeneous additive functionals of the solutions of Itô stochastic differential equations with nonregular dependence on parameter

Grigorij Kulinich Svitlana Kushnirenko Yuliia Mishura

https://doi.org/10.15559/16-VMSTA58

Pub. online: 4 Jul 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 2 (2016), pp. 191–208

Abstract

We study the asymptotic behavior of mixed functionals of the form $I_{T}(t)=F_{T}(\xi _{T}(t))+{\int _{0}^{t}}g_{T}(\xi _{T}(s))\hspace{0.1667em}d\xi _{T}(s)$, $t\ge 0$, as $T\to \infty $. Here $\xi _{T}(t)$ is a strong solution of the stochastic differential equation $d\xi _{T}(t)=a_{T}(\xi _{T}(t))\hspace{0.1667em}dt+dW_{T}(t)$, $T>0$ is a parameter, $a_{T}=a_{T}(x)$ are measurable functions such that $\left|a_{T}(x)\right|\le C_{T}$ for all $x\in \mathbb{R}$, $W_{T}(t)$ are standard Wiener processes, $F_{T}=F_{T}(x)$, $x\in \mathbb{R}$, are continuous functions, $g_{T}=g_{T}(x)$, $x\in \mathbb{R}$, are locally bounded functions, and everything is real-valued. The explicit form of the limiting processes for $I_{T}(t)$ is established under very nonregular dependence of $g_{T}$ and $a_{T}$ on the parameter T.

Asymptotic behavior of homogeneous additive functionals of the solutions of Itô stochastic differential equations with nonregular dependence on parameter

Grigorij Kulinich Svitlana Kushnirenko Yuliia Mishura

https://doi.org/10.15559/16-MSTA58

Pub. online: 4 Jul 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 2 (2016), pp. 191–208

Abstract

Large deviation principle for one-dimensional SDEs with discontinuous coefficients

Alexei Kulik Daryna Sobolieva

https://doi.org/10.15559/16-VMSTA57

Pub. online: 1 Jul 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 2 (2016), pp. 145–164

Abstract

We establish the large deviation principle for solutions of one-dimensional SDEs with discontinuous coefficients. The main statement is formulated in a form similar to the classical Wentzel–Freidlin theorem, but under the considerably weaker assumption that the coefficients have no discontinuities of the second kind.

Large deviation principle for one-dimensional SDEs with discontinuous coefficients

Alexei Kulik Daryna Sobolieva

https://doi.org/10.15559/16-MSTA57

Pub. online: 1 Jul 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 2 (2016), pp. 145–164

Abstract

Asymptotics of exponential moments of a weighted local time of a Brownian motion with small variance

Alexei Kulik Daryna Sobolieva

https://doi.org/10.15559/16-VMSTA49

Pub. online: 5 Apr 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 1 (2016), pp. 95–103

Abstract

We prove a large deviation type estimate for the asymptotic behavior of a weighted local time of $\varepsilon W$ as $\varepsilon \to 0$.

Asymptotics of exponential moments of a weighted local time of a Brownian motion with small variance

Alexei Kulik Daryna Sobolieva

https://doi.org/10.15559/16-MSTA49

Pub. online: 5 Apr 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 1 (2016), pp. 95–103

Abstract

We prove a large deviation type estimate for the asymptotic behavior of a weighted local time of $\varepsilon W$ as $\varepsilon \to 0$.

Convergence of hitting times for jump-diffusion processes

Georgiy Shevchenko

https://doi.org/10.15559/15-VMSTA32

Pub. online: 23 Sep 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 3 (2015): PRESTO-2015, pp. 203–218

Abstract

We investigate the convergence of hitting times for jump-diffusion processes. Specifically, we study a sequence of stochastic differential equations with jumps. Under reasonable assumptions, we establish the convergence of solutions to the equations and of the moments when the solutions hit certain sets.

Convergence of hitting times for jump-diffusion processes

Georgiy Shevchenko

https://doi.org/10.15559/15-MSTA32

Pub. online: 23 Sep 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 3 (2015): PRESTO-2015, pp. 203–218

Detailed search

Search results 38

Export citation

Copy and paste formatted citation

Download citation in file

Authors