Global ETD Search

1	Random processes in truncated and ordinary Weyl chambers Schmid, Patrick 15 March 2011 (has links) (PDF) The work consists of two parts. In the first part which is concerned with random walks, we construct the conditional versions of a multidimensional random walk given that it does not leave the Weyl chambers of type C and of type D, respectively, in terms of a Doob h-transform. Furthermore, we prove functional limit theorems for the rescaled random walks. This is an extension of recent work by Eichelsbacher and Koenig who studied the analogous conditioning for the Weyl chamber of type A. Our proof follows recent work by Denisov and Wachtel who used martingale properties and a strong approximation of random walks by Brownian motion. Therefore, we are able to keep minimal moment assumptions. Finally, we present an alternate function that is amenable to an h-transform in the Weyl chamber of type C. In the second part which is concerned with Brownian motion, we examine the non-exit probability of a multidimensional Brownian motion from a growing truncated Weyl chamber. Different regimes are identified according to the growth speed, ranging from polynomial decay over stretched-exponential to exponential decay. Furthermore we derive associated large deviation principles for the empirical measure of the properly rescaled and transformed Brownian motion as the dimension grows to infinity. Our main tool is an explicit eigenvalue expansion for the transition probabilities before exiting the truncated Weyl chamber. Irrfahrten Weylkammern Dysons Brown\'sche Bewegung Konditionierung Karlin-McGregor Formel Eigenwertexpansion. Reduite Nichtkollisionswahrscheinlichkeit Nichtaustrittswahrscheinlichkeit random walks Weyl chambers Dyson\'s Brownian motion conditioning non-colliding Brownian motions Karlin-McGregor formula eigenvalue expansion reduite non-colliding probability non-exit probability ddc:500
2	Random processes in truncated and ordinary Weyl chambers: Random processes in truncated and ordinary Weylchambers Schmid, Patrick 03 September 2011 (has links) The work consists of two parts. In the first part which is concerned with random walks, we construct the conditional versions of a multidimensional random walk given that it does not leave the Weyl chambers of type C and of type D, respectively, in terms of a Doob h-transform. Furthermore, we prove functional limit theorems for the rescaled random walks. This is an extension of recent work by Eichelsbacher and Koenig who studied the analogous conditioning for the Weyl chamber of type A. Our proof follows recent work by Denisov and Wachtel who used martingale properties and a strong approximation of random walks by Brownian motion. Therefore, we are able to keep minimal moment assumptions. Finally, we present an alternate function that is amenable to an h-transform in the Weyl chamber of type C. In the second part which is concerned with Brownian motion, we examine the non-exit probability of a multidimensional Brownian motion from a growing truncated Weyl chamber. Different regimes are identified according to the growth speed, ranging from polynomial decay over stretched-exponential to exponential decay. Furthermore we derive associated large deviation principles for the empirical measure of the properly rescaled and transformed Brownian motion as the dimension grows to infinity. Our main tool is an explicit eigenvalue expansion for the transition probabilities before exiting the truncated Weyl chamber. info:eu-repo/classification/ddc/500 ddc:500

Search results

Random processes in truncated and ordinary Weyl chambers

Random processes in truncated and ordinary Weyl chambers: Random processes in truncated and ordinary Weylchambers