Existence and uniqueness theorems for solutions of McKean–Vlasov stochastic equations
- Y. Mishura, A. Veretennikov
- MathematicsTheory of Probability and Mathematical Statistics
- 7 March 2016
New weak and strong existence and weak and strong uniqueness results for multi-dimensional stochastic McKean--Vlasov equations are established under relaxed regularity conditions. Weak existence is a…
On hedging European options in geometric fractional Brownian motion market model
- E. Azmoodeh, Y. Mishura, E. Valkeila
- Mathematics
- 2009
We work with fractional Brownian motion with Hurst index H > 1/2. We show that the pricing model based on geometric fractional Brownian motion behaves to certain extend as a process with bounded…
Fractional Cox–Ingersoll–Ross process with non-zero «mean»
- Y. Mishura, Anton YURCHENKO-TYTARENKO
- Mathematics
- 5 March 2018
In this paper we define the fractional Cox–Ingersoll–Ross process as $X_t:=Y_t^2\mathbf{1}_{\{t 0:Y_s=0\}\}}$, where the process $Y=\{Y_t,t\ge0\}$ satisfies the SDE of the form…
Theory and Statistical Applications of Stochastic Processes
- Y. Mishura, G. Shevchenko
- Mathematics
- 4 January 2018
This book is concerned with the theory of stochastic processes and the theoretical aspects of statistics for stochastic processes. It combines classic topics such as construction of stochastic…
Bounds for expected maxima of Gaussian processes and their discrete approximations
- K. Borovkov, Y. Mishura, A. Novikov, M. Zhitlukhin
- Mathematics
- 1 August 2015
The paper deals with the expected maxima of continuous Gaussian processes that are Hölder continuous in -norm and/or satisfy the opposite inequality for the -norms of their increments. Examples of…
Constructing functions with prescribed pathwise quadratic variation
- Y. Mishura, A. Schied
- Mathematics
- 15 November 2015
Fractional Lévy Processes as a Result of Compact Interval Integral Transformation
- H. Tikanmäki, Y. Mishura
- Mathematics
- 3 February 2010
Fractional Brownian motion can be represented as an integral of a deterministic kernel w.r.t. an ordinary Brownian motion either on infinite or compact interval. In previous literature fractional…
Hypothesis testing of the drift parameter sign for fractional Ornstein-Uhlenbeck process
- A. Kukush, Y. Mishura, K. Ralchenko
- Mathematics
- 10 April 2016
We consider the fractional Ornstein-Uhlenbeck process with an unknown drift parameter and known Hurst parameter $H$. We propose a new method to test the hypothesis of the sign of the parameter and…
Statistics of stochastic processes
- D. Gusak, A. Kukush, A. Kulik, Y. Mishura, A. Pilipenko
- Mathematics
- 2010
General statement of the problem of testing two hypotheses Let the trajectory \(x(\cdot)\) of a stochastic process \(\{X(t), t\in[0,T]\}\) be observed.
Approximation Schemes for Stochastic Differential Equations in Hilbert Space
- Y. Mishura, G. Shevchenko
- Mathematics
- 28 August 2007
For solutions of Ito–Volterra equations and semilinear evolution-type equations we consider approximations via the Milstein scheme, approximations by finite-dimensional processes, and approximations…
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