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Functionals of Telegraph Process
This chapter is devoted to the various functionals of telegraph processes. First, we present well-known results on distributions of the telegraph...
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Symmetric Telegraph Process on the Line
The symmetric Goldstein-Kac telegraph process describes the motion of a particle on the real line moving at some finite constant speed and...
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Telegraph Processes and Option Pricing
This book provides an extensive, systematic overview of the modern theory of telegraph processes and their multidimensional counterparts, together...
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Asymmetric Jump-Telegraph Processes
The concepts and results of Chap. 2 are generalised, first, to asymmetric processes equipped with jumps (of...
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Financial Modelling Based on Telegraph Processes
This last chapter of the book is devoted to financial applications of the previously described results. After brief preliminaries, the chapter opens...
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Telegraph-Type Processes in Higher Dimensions
In recent decades, finite-velocity stochastic motions in Euclidean spaces of various dimensions have been extensively studied. This chapter provides...
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Some Results on the Telegraph Process Confined by Two Non-Standard Boundaries
We analyze the one-dimensional telegraph random process confined by two boundaries, 0 and H > 0. The process experiences hard reflection at the...
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On Estimation for Brownian Motion Governed by Telegraph Process with Multiple Off States
Brownian motion whose infinitesimal variance changes according to a three-state continuous-time Markov Chain is studied. This Markov Chain can be...
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Asymptotic Results for the Absorption Time of Telegraph Processes with Elastic Boundary at the Origin
We consider a telegraph process with elastic boundary at the origin studied recently in the literature (see e.g. Di Crescenzo et al. (Methodol Comput...
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Kac-Ornstein-Uhlenbeck Processes: Stationary Distributions and Exponential Functionals
We study Ornstein-Uhlenbeck processes whose parameters are modulated by an external two-state Markov process. The conditional means of such a process...
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First Crossing Times of Telegraph Processes with Jumps
The paper presents exact formulae related to the distribution of the first passage time τ x of the jump-telegraph process. In particular, the Laplace...
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Ornstein-Uhlenbeck Processes of Bounded Variation
Ornstein-Uhlenbeck process of bounded variation is introduced as a solution of an analogue of the Langevin equation with an integrated telegraph...
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Jump-Diffusion Processes with Regime Switching
In this chapter, we examine a modification of the standard steady state process obtained by adding a diffusion component. We give a detailed...
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Telegraph Process with Elastic Boundary at the Origin
We investigate the one-dimensional telegraph random process in the presence of an elastic boundary at the origin. This process describes a...
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On ruin probabilities with risky investments in a stock with stochastic volatility
We investigate the asymptotic of ruin probabilities when the company combines the life- and non-life insurance businesses and invests its reserve...
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Discretely Observed Brownian Motion Governed by Telegraph Process: Estimation
A Brownian motion whose infinitesimal variance alternates according to a telegraph process is considered. This stochastic process can be employed to...
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Combining sentiment analysis classifiers to explore multilingual news articles covering London 2012 and Rio 2016 Olympics
This study aims to present an approach for the challenges of working with Sentiment Analysis (SA) applied to news articles in a multilingual corpus....
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Preliminaries
In this chapter, we establish the prerequisites for the book by recalling some basic notions and concepts of probability and calculus.
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Permutation Entropy as the Measure of Globalization Process
The applicationMiśkiewicz, Janusz of permutation entropy as the globalization measure is discussed within this paper. In order to verify the stated...