Total shift during the first passages of Markov-modulated Brownian motion with bilateral ph-type jumps: Formulas driven by the minimal solution matrix of a Riccati equation

2016 ◽  
Vol 32 (3) ◽  
pp. 433-459 ◽  
Author(s):  
Soohan Ahn
Keyword(s):  
Brownian Motion ◽  
Riccati Equation ◽  
Minimal Solution ◽  
Markov Modulated ◽  
Solution Matrix ◽  
Total Shift

scholarly journals Occupation Times for Markov-Modulated Brownian Motion

2012 ◽  
Vol 49 (02) ◽  
pp. 549-565 ◽  
Author(s):  
Lothar Breuer
Keyword(s):  
Brownian Motion ◽  
First Passage Time ◽  
Passage Time ◽  
Laplace Transforms ◽  
Occupation Times ◽  
First Passage ◽  
Scale Functions ◽  
Positive Variation ◽  
Markov Modulated

In this paper we determine the distributions of occupation times of a Markov-modulated Brownian motion (MMBM) in separate intervals before a first passage time or an exit from an interval. We derive the distributions in terms of their Laplace transforms, and we also distinguish between occupation times in different phases. For MMBMs with strictly positive variation parameters, we further propose scale functions.

A Brownian motion with two reflecting barriers and Markov-modulated speed

2004 ◽  
Vol 41 (04) ◽  
pp. 1237-1242 ◽  
Author(s):  
Offer Kella ◽  
Wolfgang Stadje
Keyword(s):  
Brownian Motion ◽  
Markov Chain ◽  
Linear Algebra ◽  
Stationary Distribution ◽  
The State ◽  
Long Run ◽  
Markov Modulated ◽  
Two Barriers ◽  
Reflecting Barriers

We consider a Brownian motion with time-reversible Markov-modulated speed and two reflecting barriers. A methodology depending on a certain multidimensional martingale together with some linear algebra is applied in order to explicitly compute the stationary distribution of the joint process of the content level and the state of the underlying Markov chain. It is shown that the stationary distribution is such that the two quantities are independent. The long-run average push at the two barriers at each of the states is also computed.

A Brownian motion with two reflecting barriers and Markov-modulated speed

2004 ◽  
Vol 41 (4) ◽  
pp. 1237-1242 ◽  
Author(s):  
Offer Kella ◽  
Wolfgang Stadje
Keyword(s):  
Brownian Motion ◽  
Markov Chain ◽  
Linear Algebra ◽  
Stationary Distribution ◽  
The State ◽  
Long Run ◽  
Markov Modulated ◽  
Two Barriers ◽  
Reflecting Barriers

We consider a Brownian motion with time-reversible Markov-modulated speed and two reflecting barriers. A methodology depending on a certain multidimensional martingale together with some linear algebra is applied in order to explicitly compute the stationary distribution of the joint process of the content level and the state of the underlying Markov chain. It is shown that the stationary distribution is such that the two quantities are independent. The long-run average push at the two barriers at each of the states is also computed.

scholarly journals Occupation Times for Markov-Modulated Brownian Motion

2012 ◽  
Vol 49 (2) ◽  
pp. 549-565 ◽  
Author(s):  
Lothar Breuer
Keyword(s):  
Brownian Motion ◽  
First Passage Time ◽  
Passage Time ◽  
Laplace Transforms ◽  
Occupation Times ◽  
First Passage ◽  
Scale Functions ◽  
Positive Variation ◽  
Markov Modulated

In this paper we determine the distributions of occupation times of a Markov-modulated Brownian motion (MMBM) in separate intervals before a first passage time or an exit from an interval. We derive the distributions in terms of their Laplace transforms, and we also distinguish between occupation times in different phases. For MMBMs with strictly positive variation parameters, we further propose scale functions.

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